Due to requirements on memory and higher-order derivatives, MAML with Implicit Gradients (iMAML) was proposed in [1]} to address the challenge of differentiating through the long optimization path in MAML. In addition to that, iMAML proposes to incorporate regularization into the problem formulation to enable appropriate leaning in the inner level, while preventing over-fitting. In this case, the inner-level problem is formulated as
\(\underset{{\mathbf {\phi }}}{\min }~\mathcal {L}({\mathbf {\phi }}, \mathcal {D}^{\mathrm {tr}}_i) + \frac{\lambda }{2}~||{\mathbf {\phi }}- {\mathbf {\theta }}||^2,\) 
